Seminarium Teorii Względności i Grawitacji

In classical general relativity, the gravitational collapse of matter inevitably leads to the formation of a spacetime singularity. Numerous works have shown that introducing loop quantum gravity corrections at the semiclassical level resolves the singularity by replacing it with a bounce. Nevertheless, a fully quantum treatment of the problem has remained largely unexplored.In this talk, I will present the loop quantization of the marginally bound Lemaître-Tolman-Bondi dust model, providing a fully quantum treatment of its dynamics.The key feature that allows the direct quantization is the classical deparametrization of the system into independently evolving shells, each of which can be quantized separately. Through a numerical analysis, I will show that every shell undergoes a unitary evolution avoiding the singularity by means of a bounce. Finally, I will discuss the expectation values of the volume and density operators in order to draw a comparison with the semiclassical limit aforementioned.